When movement outcome differs consistently from the intended movement, errors are used to correct subsequent movements (e.g., adaptation to displacing prisms or force fields) by updating an internal model of motor and/or sensory systems. Here, we examine changes to an internal model of the motor system under changes in the variance structure of movement errors lacking an overall bias. We introduced a horizontal visuomotor perturbation to change the statistical distribution of movement errors anisotropically, while monetary gains/losses were awarded based on movement outcomes. We derive predictions for simulated movement planners, each differing in its internal model of the motor system. We find that humans optimally respond to the overall change in error magnitude, but ignore the anisotropy of the error distribution. Through comparison with simulated movement planners, we found that aimpoints corresponded quantitatively to an ideal movement planner that updates a strictly isotropic (circular) internal model of the error distribution. Aimpoints were planned in a manner that ignored the direction-dependence of error magnitudes, despite the continuous availability of unambiguous information regarding the anisotropic distribution of actual motor errors.